Use circle graphs to compare parts of a clearly defined whole

Learning goal: Read and construct a circle graph that shows each category's share of one complete data set. Before comparing slices, identify the whole, the category definitions and the units. A visually large sector is meaningful only in relation to the circle it belongs to.

A fictional community event uses forty volunteer hours: twenty for setup, ten for food preparation, six for games and four for cleanup. The whole is forty hours, not forty volunteers or forty dollars. Each hour is assigned to exactly one category so the categories do not overlap, and together they account for all forty hours.

Setup takes twenty of forty hours, or one half. Food preparation takes ten of forty, or one fourth. Games take six of forty, or fifteen hundredths, and cleanup takes four of forty, or one tenth. These shares total one whole: fifty percent plus twenty-five percent plus fifteen percent plus ten percent equals one hundred percent. Percent means parts per hundred; it provides another way to express the same shares.

In the diagram, the setup sector occupies half the circle and food occupies a quarter. Games occupies a larger sector than cleanup because six hours exceeds four. A circle has 360 degrees around its center, so one half corresponds to 180 degrees and one quarter to ninety degrees. The six-hour and four-hour sectors correspond to fifty-four and thirty-six degrees. Equal numerical shares must occupy equal portions of the circle.

Labels should include the category and either its count, fraction or percentage, with enough information to recover the meaning. A key can connect colors or patterns to categories, but color alone is insufficient when a reader cannot distinguish the shades. Title the graph with its place, time and measured whole, especially when several graphs appear together.

Circle graphs help answer proportion questions. Setup takes twice as much time as food preparation because twenty is twice ten. Setup and cleanup together take twenty-four of forty hours, or three fifths. Games and cleanup together take ten hours, the same share as food preparation. Use numerical relationships to check the drawing rather than estimating every answer from its shape.

The same fraction can represent different amounts in different wholes. Half of forty hours is twenty hours; half of sixty hours is thirty hours. Two half-circle sectors can look identical while representing different absolute totals. When comparing communities or years, read both totals before saying that equal-looking sectors mean equal hours or money.

A circle graph is a poor choice for categories that overlap. If people can choose both games and music as favorite activities, adding the response counts may exceed the number of people. Those counts are not separate pieces of one participant whole. A labeled bar graph may be more appropriate. Similarly, separate monthly totals do not become parts of one month merely by being drawn in a circle.

Check for misleading omissions. If the event also used five unreported transport hours, the forty-hour circle is incomplete unless its title explicitly excludes transport. A three-dimensional drawing can make front sectors appear larger than their true shares. Use a flat, accurately divided circle and report missing or excluded data clearly.

Worked calculation: Games plus cleanup use 6 + 4 = 10 hours. Their combined share is 10/40 = 1/4, matching food preparation. The total hours, fraction and sector size should agree.

Worked critique: A second event uses sixty hours, half for setup. Its setup sector matches the first event's half-circle, but it represents thirty hours rather than twenty. The second event uses ten more setup hours despite the equal proportions.

Guided performance: Sort a provided forty-card set into the four fictional hour categories, checking that every card belongs to exactly one group. Build a circle graph with an adult-supported template or graphing tool. Check the half and quarter first, then verify the remaining sectors and labels.

Independent performance: Collect or use a clearly identified data set with mutually exclusive categories, state the whole and make a labeled circle graph. Answer one part-to-whole and one combined-category question. Compare it with a graph using a different total, explaining both the proportions and actual amounts. Revise any overlapping categories or missing data before publishing your display.